has to be well-behaved with reasonable probability. That can only happen if \(\Vert X\Vert _2^2\)  exhibits a sufficiently strong concentration around its mean—a so-called thin-shell bound. Thin-shell bounds are known for a variety of random vectors (for estimates in the log-concave case, see, e.g. [1]}, [2]}, [3]} and Corollary REF , below).
